Such roller screw drives for converting a rotational motion into a translational motion are used mainly in cases in which, for operational reasons, no high precision of pitch and position is required but rather, an economic solution with a high degree of efficiency and good bearing capacity. Such a roller screw drive is known from DE-OS 21 50 739. This drive comprises a solid nut body and two likewise solid annular cam members which mesh by regions having annular cam surfaces with annular end recesses of a cage for the rollers. The manufacturing of this device is highly complicated so that the resulting construction is very expensive.